Average Error: 6.1 → 5.9
Time: 10.4s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[x - \frac{y}{\frac{a}{z - t}}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
x - \frac{y}{\frac{a}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r211766 = x;
        double r211767 = y;
        double r211768 = z;
        double r211769 = t;
        double r211770 = r211768 - r211769;
        double r211771 = r211767 * r211770;
        double r211772 = a;
        double r211773 = r211771 / r211772;
        double r211774 = r211766 - r211773;
        return r211774;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r211775 = x;
        double r211776 = y;
        double r211777 = a;
        double r211778 = z;
        double r211779 = t;
        double r211780 = r211778 - r211779;
        double r211781 = r211777 / r211780;
        double r211782 = r211776 / r211781;
        double r211783 = r211775 - r211782;
        return r211783;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.1
Target0.7
Herbie5.9
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753216593153715602325729 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if a < -193800797444951.66

    1. Initial program 9.6

      \[x - \frac{y \cdot \left(z - t\right)}{a}\]
    2. Using strategy rm

    3. Applied associate-/l*0.6

      \[\leadsto x - \color{blue}{\frac{y}{\frac{a}{z - t}}}\]
    4. Using strategy rm

    5. Applied clear-num0.6

      \[\leadsto x - \color{blue}{\frac{1}{\frac{\frac{a}{z - t}}{y}}}\]

    if -193800797444951.66 < a < 8.525965780747699e-40

    1. Initial program 0.8

      \[x - \frac{y \cdot \left(z - t\right)}{a}\]

    if 8.525965780747699e-40 < a

    1. Initial program 8.7

      \[x - \frac{y \cdot \left(z - t\right)}{a}\]
    2. Using strategy rm

    3. Applied associate-/l*0.7

      \[\leadsto x - \color{blue}{\frac{y}{\frac{a}{z - t}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification5.9

    \[\leadsto x - \frac{y}{\frac{a}{z - t}}\]

Reproduce

herbie shell --seed 2019298 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :herbie-target
  (if (< y -1.07612662163899753e-10) (- x (/ 1 (/ (/ a (- z t)) y))) (if (< y 2.8944268627920891e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

  (- x (/ (* y (- z t)) a)))